ABSTRACT：It
is very difficult to solve Maximum Mutual Information (MMI) or Maximum
Likelihood (ML) for all possible Shannon Channels or uncertain rules of
choosing hypotheses, so that we have to use iterative methods. According
to the Semantic Mutual Information (SMI) and R(G)
function proposed by Chenguang Lu (1993) (where R(G)
is an extension of information rate distortion function R(D),
and G is the
lower limit of the SMI), we can obtain a new iterative algorithm of
solving the MMI and ML for tests, estimations, and mixture models. The
SMI is defined by the average log normalized likelihood. The likelihood
function is produced from the truth function and the prior by the
semantic Bayesian inference. A group of truth functions constitute a
semantic channel. Letting the semantic channel and Shannon channel
mutually match and iterate, we can obtain the Shannon channel that
maximizes the Shannon mutual information and the average log likelihood.
This iterative algorithm is called Channels’ Matching algorithm or the
CM algorithm. The convergence can be intuitively explained and proved by
the R(G)
function. Several iterative examples for tests, estimations, and mixture
models show
that the computation of the CM algorithm is simple, and can be
demonstrated in excel files. For most random examples, the numbers of
iterations for convergence are close to 5. For mixture models, the CM algorithm is
similar to the EM algorithm; however, the CM algorithm has better
convergence and more potential applications in comparison with the
standard EM algorithm.